The equation of a parabola is y = x^2 - 2x + 2. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions. ______

Identify Vertex Form: Identify the vertex form of a parabola. The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete the Square: Complete the square to rewrite the given equation y = x^2 - 2x + 2 in vertex form. First, we need to create a perfect square trinomial from the quadratic part of the equation. To do this, we take half of the coefficient of x, which is -2, divide it by 2 to get -1, and then square it to get 1. We will add and subtract this value inside the equation.Add and Subtract: Add and subtract the square of half the coefficient of x inside the equation. The equation becomes y = x^2 - 2x + 1 - 1 + 2. We added and subtracted 1 to complete the square while keeping the equation balanced.Rewrite Equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. The equation now looks like y = (x^2 - 2x + 1) + (2 - 1). This simplifies to y = (x - 1)^2 + 1, which is now in vertex form.

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The equation of a parabola is $y = x^2 - 2x + 2$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Algebra 1

Write a quadratic function in vertex form

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Q. The equation of a parabola is

y = x^2 - 2x + 2

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

______

Identify Vertex Form: Identify the vertex form of a parabola. The vertex form of a parabola is given by $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete the Square: Complete the square to rewrite the given equation $y = x^2 - 2x + 2$ in vertex form. $\newline$ First, we need to create a perfect square trinomial from the quadratic part of the equation. To do this, we take half of the coefficient of $x$ , which is $-2$ , divide it by $2$ to get $-1$ , and then square it to get $1$ . We will add and subtract this value inside the equation.
Add and Subtract: Add and subtract the square of half the coefficient of $x$ inside the equation. $\newline$ The equation becomes $y = x^2 - 2x + 1 - 1 + 2$ . $\newline$ We added and subtracted $1$ to complete the square while keeping the equation balanced.
Rewrite Equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. $\newline$ The equation now looks like $y = (x^2 - 2x + 1) + (2 - 1)$ . $\newline$ This simplifies to $y = (x - 1)^2 + 1$ , which is now in vertex form.